Variations in the isotropic bulk magnetic susceptibility, which introduce spatially varying local fields, are a fundamental complication for NMR studies of spatially heterogeneous samples. These local fields are reflected in frequency shifts, resulting in increases in the spectral linewidths and background gradients that interfere with spin echo measurements of the spin-spin relaxation time and molecular diffusion rate. Such effects are well documented and they lead to a decrease in spectral resolution, non-linearities (distortions) in NMR imaging and incorrect measurements of molecular diffusion rates in pulsed gradient measurements. Magic Angle Spinning (MAS) has previously been shown to remove the time-averaged frequency shifts via coherent averaging. This has resulted in a variety of applications of high-resolution MAS studies to complex samples, where the primary role of MAS is to remove the susceptibility broadening. Here we demonstrate that signal attenuation due to molecular diffusion in background gradient may be also suppressed via MAS.